Lyotropic liquid crystal (LLC) assemblies have garnered widespread attention in disparate areas of chemistry, by virtue of their utility in highly selective chemical separations such as water desalination and selective ion-transporting membranes, as templates for mesoporous inorganic materials, as media for biophysical studies of transmembrane proteins (“cubic lipidic phases”), and as therapeutic nucleic acid delivery vehicles. See, e.g., (1) Kato, T.; Mizoshita, N.; Kishimoto, K. Angew. Chem. Int. Ed. 2006, 45, 38; (2) Zhou, M.; Nemade, P. R.; Lu, X.; Zeng, X.; Hatakeyama, E. S.; Noble, R. D.; Gin, D. L. J. Am. Chem. Soc. 2007, 129, 9574; (3) Kerr, R. L.; Miller, S. A.; Shoemaker, R. K.; Elliott, B. J.; Gin, D. L. J. Am. Chem. Soc. 2009, 131, 15972; (4) Hentze, H. P.; Kramer, E.; Berton, B.; Förster, S.; Antonietti, M.; Dreja, M. Macromolecules 1999, 32, 5803; (5) Johansson, L. C.; Woehri, A. B.; Katona, G.; Engstroem, S.; Neutze, R. Curr. Opin. Struct. Biol. 2009, 19, 372; (6) Rummel, G.; Hardmeyer, A.; Widmer, C.; Chiu, M. L.; Nollert, P.; Locher, K. P.; Pedruzzi, I.; Landau, E. M.; Rosenbusch, J. P. J. Struct. Biol. 1998, 121, 82; and (7) Leal, C.; Bouxsein, N. F.; Ewert, K. K.; Safinya, C. R. J. Am. Chem. Soc. 2010, 132, 16841. LLCs form by the concentration-dependent supramolecular self-organization of amphiphilic molecules in water or another polar solvent into soft materials having distinct hydrophilic and hydrophobic nanoscale domains (˜7 to 100 Å) with long-range periodic order. See (8) Fairhurst, C. E.; Fuller, S.; Gray, J.; Holmes, M. C.; Tiddy, G. J. T. In Handbook of Liquid Crystals, Demus, D.; Goodby, J. W.; Gray, G. W.; Spiess, H. W.; Vill, V., Eds.; Wiley-VCH: Weinheim, 1998; Vol. 3, pp 341. LLCs typically exhibit ordered phases such as lamellae (Lα), bicontinuous cubic (Q; e.g., double gyroid, double diamond, and “Plumber's Nightmare”), hexagonally packed cylinders (H), and discontinuous cubic (I; e.g., body-centered cubic) morphologies. See (9) Shearman, G. C.; Tyler, A. I. I.; Brooks, N. J.; Templer, R. H.; Ces, O.; Law, R. V.; Seddon, J. M. Liq. Cryst. 2010, 37, 679. High symmetry Q-phase assemblies, exemplified by the double gyroid (G) phase, are particularly desirable for membrane applications by virtue of their interpenetrating hydrophilic and hydrophobic domains that percolate over macroscopic lengthscales with tunable nanopore diameters (˜7 to 50 Å) and well-defined nanopore functionalities. Q-phases typically exist only in limited polar solvent concentration and temperature phase windows, due to the fact that their interfaces substantially deviate from a constant mean interfacial curvature. See (10) Pindzola, B. A.; Gin, D. L. Langmuir 2000, 16, 6750; (11) Matsen, M. W.; Bates, F. S. Macromolecules 1996, 29, 7641; and (12) Shearman, G. C.; Khoo, B. J.; Motherwell, M. L.; Brakke, K. A.; Ces, O.; Conn, C. E.; Seddon, J. M.; Templer, R. H. Langmuir 2007, 23, 7276. While “critical packing parameter” models enable correlations of amphiphile structure with the formation of constant mean curvature Lα, H, and I phases, these models fail to provide reliable and general molecular design criteria for amphiphiles that form non-constant mean curvature Q phases. See (13) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991; (14) Svenson, S. J. Dispersion Sci. Technol. 2004, 25, 101; and (15) Diamant, H.; Andelman, D. In Surfactant Science Series, Zana, R.; Xia, J., Eds.; Marcel Dekker, Inc.: New York, 2004; Vol. 117, pp 37. Gin and co-workers recently reported that small molecule quaternary ammonium, phosphonium, and imidazolium Gemini amphiphiles, derived from dimerizing single-tail surfactants with an alkyl spacer through the ionic headgroup, exhibit a greater tendency to form G phase LLCs in water. See (16) Alami, E.; Levy, H.; Zana, R.; Skoulios, A. Langmuir 1993, 9, 940; (17) Hatakeyama, E. S.; Wiesenauer, B. R.; Gabriel, C. J.; Noble, R. D.; Gin, D. L. Chem. Mater. 2010, 22, 4525; (18) Pindzola, B. A.; Jin, J.; Gin, D. L. J. Am. Chem. Soc. 2003, 125, 2940; (19) Gin, D. L.; Zhou, M.; Noble, R. D.; Bara, J. E.; Kerr, R. L.; Wiesenauer, B. R. US Patent Appl 2009/0173693, 2009; and (20) Menger, F. M.; Keiper, J. S. Angew. Chem. Int. Ed. 2000, 39, 1906. The notion that Gemini architectures universally form bicontinuous cubic LLC morphologies remains an untested amphiphile design principle.